Addressing the health needs of a growing and ageing population is a central challenge facing modern society. Technology is enabling the collection of increasingly large and heterogeneous biomedical data sets, yet interpreting such data to gain knowledge about disease mechanisms and clinical and preventative strategies is still a major open problem. Artificial Intelligence (AI) techniques hold huge promise to provide an integrative framework for extracting knowledge from data, with a high potential for fundamental and clinical breakthroughs with significant impact both on public health and on the future of the UK bioeconomy. The ambition of the proposed CDT is to train a cadre of highly skilled interdisciplinary scientists who will spearhead the development and deployment of AI techniques in the biomedical sector. Achieving our long-term aims will require several hurdles to be overcome. The biomedical sector poses unique methodological challenges to AI technology, due to the need of interpretable models which can quantify uncertainties within predictions. It also presents formidable cultural and technical language barriers, requiring honed communication skills to overcome disciplinary boundaries. Perhaps most importantly, it requires researchers and practitioners with a keen awareness of the societal, legal and ethical dimension of their research, who are able to reach out to societal stakeholders, and to anticipate and engage with the potential issues arising from deploying AI technology in the biomedical sector. We will realise our ambition through a structured training programme: students will initially acquire the foundational skills in a Master by Research first year, which includes taught courses on the technical, biomedical and socio-ethical aspects of biomedical AI, and provides multiple opportunities to directly experience interdisciplinary research through rotation projects. Students will then acquire in depth research experience through an interdisciplinary PhD, bridging between the University of Edinburgh's world-leading institutions pursuing informatics and biomedical research. Students will benefit from a large and exceptionally distinguished faculty of potential supervisors: over 60 academics including several fellows of the Royal Society/ Royal Society of Edinburgh, and over forty recipients of prestigious fellowships from the ERC, the research councils, and biomedical charities such as the Wellcome Trust. This training programme will be interleaved with intensive training in interdisciplinary communication and science communication, and will offer multiple opportunities to engage with external stakeholders including industrial and NHS internships.